1. Field of the Invention
The present invention relates to frequency synthesis and more particularly to direct digital synthesizers employing look-up tables for converting phase data into an amplitude of a periodic function. The invention further relates to a method and apparatus for converting incremental phase values into sine amplitude numbers employing a series expansion technique for increasing output accuracy per unit memory size.
2. Background of the Art
The commercial viability of advanced digital communication systems involving remote or mobile users and relay systems depends on several key design factors and user requirements. Circuit elements must provide high speed data transfer with high frequency accuracy or resolution to accommodate a large number of users. The circuitry needs to be relatively inexpensive to manufacture while being highly reliable and consume a minimum amount of power to present a low drain on mobile users.
Direct Digital Synthesizer (DDS) circuits are very useful as reference or carrier wave frequency sources for advanced digital communication applications. DDS circuits can be built as large scale integrated circuits to reduce power consumption while using a relatively low number of discrete components or internal parts to increase reliability, reduce production costs, and maintain high speed and high resolution operation.
Direct Digital Synthesizers generally accumulate phase data in the form of discrete increments of phase in an accumulator from which they are transferred on a periodic basis to a phase to amplitude converter. The phase data is then correlated with an amplitude which corresponds to the amplitude of a desired periodic function at that phase. That is, a chosen periodic function, typically a sine wave, has a given amplitude at a given phase and amplitude values are selected for each input phase value accordingly. The selection or conversion process generally utilizes a sine look-up table stored in a Read Only Memory (ROM) circuit which contains preselected amplitudes corresponding to given phase positions of the periodic function.
The spectral purity of the DDS output is determined by the accuracy or resolution of amplitude values stored in ROM and quantization errors in the phase to amplitude conversion and digital-to-analog conversion steps. The resolution of the digital to analog conversion as well as the generation of spurious noise is also dependent upon the resolution of the input data to the DAC. That is, for n-bit wide digital amplitude input data the output noise level decreases a related amount per bit width, typically on the order of 6 dB per DAC input bit. A 12 bit DAC input, or amplitude output, would provide about a 72 dB drop in the power level of noise spurs. Therefore, it is desirable to increase the resolution of the ROM output to decrease quantization errors in the DAC stage and decrease spurious noise. This means the amplitude values need to be defined or stored in the ROM in as high a resolution or bit width as possible to decrease noise.
However, the higher the resolution of the amplitude values or larger bit size, the larger the ROM. Unfortunately, larger ROM storage means higher power consumption, larger parts count in the ROM structure, lower reliability, lower speed, and greatly increased costs. Increasing ROM size to achieve improved resolution provides a diminishing return in terms of related operating parameters for the DDS. Therefore, the DDS is constructed with a more limited resolution to optimize other factors such as cost.
A few techniques have been developed in an attempt to decrease quantization errors during sine conversion and increase the effective resolution. One such technique is shown in "A Digital Frequency Synthesizer", J. Tierney, IEEE Trans. Audio. Electroacoust., Vol AU-19, p 48, March 1971, in which the input phase data is divided into two phase angles whose amplitudes are computed and summed together to provide the final output. Another technique is disclosed in "CMOS/SOS Frequency Synthesizer LSI Circuit for Spread Spectrum Communications", D. A. Sunderland, et. al, IEEE Journal of Solid-State Circuits, Vol SC-19, No. 4, pp. 497-505, August 1984, where three phase angles are converted to small amplitude increments which are summed together. While these approaches have helped with quantization errors arising from the ROM conversion process, they have not greatly increased the accuracy of the output of the amplitude conversion process.
High accuracy is needed in addition to high resolution in order to provide an advanced communications frequency source. That is, even with resolution high and spurious noise reduced to a minimum, the accuracy to which the frequency is known must also be high. High accuracy in is required to provide error free fine tuning for accurate and reproducible frequency selection in advanced communications.
Accuracy can also be increased by increasing the bit width of the data stored in ROM. However, as before, this degrades the overall performance of the conversion process and apparatus. An alternative is to provide circuitry for performing pure computation, without look-up tables, of the amplitude values directly from input phase values. This can be accomplished with very high degrees of accuracy. Computational processes, however, are much slower and decrease the speed of the sine conversion process. At the same time, purely computational circuits generally require additional area for the various internal components used.
What is needed is a method and apparatus for converting phase data to amplitude data with high accuracy and resolution output for a minimum of memory size. The method should perform the conversion at the high speeds associated with look-up tables but with increased accuracy associated with purely computational circuits. A conversion apparatus is needed to implement this method, which generates a high accuracy output at very high clock rates with a minimum of circuit area or components.